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Chapitre 1 Quelques mots de V* sur V={a, b, c}: (, a, b, c, aa, ab, ba, bb, aaa, aab, abccbbaabcaacb, . V* c@EEE>_(*b'C$Eƀb' & FG??KL/01:>EGHXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{         $ % & @@A@A@A<@@4]@4g@6gA @A8g@4@AnATnAjAhA&hA(hAPhARhAThAVn@pAnnArnAtnAnAn@@A(j@*jA,jA.jA0jA2j@4jA6jA8jA:jAjA@j@Bj@DjAFjAHjAJjALjANjAPjARjATjAVjAXjAZjA\jA^jA`jAbj@v@@x@@z@A@@z@A@Ap@@Ayz CHAPITRE 4mlml FMicrosoft Word DocumentNB6WWord.Document.8 ՜.+,D՜.+,< hp  'lirmmE  CHAPITRE 4 Title 6> _PID_GUID'AN{D4F2FB80-5D26-11D2-87C6-D0416AD1D162}w|Gds |iR|0|j|1 Oh+'0d    , 8DLT\' CHAPITRE 4 HAPmlPlPNormalEmlm236Microsoft Word 8.0d@CP1@l ks@Z@V_0WH:#SH<#Th\:#wRh]8J#Sh^dWxSxgXxgSz ^UhmWhnWhoRhp8Rhq n|Zdw|[d|Kv|Ldj|Mdo|Ndxz >pxp2  xzxt |n, |o|58|6x|7cncQc S cX R B#UD#W@#, cad un nombre de la forme 2n b*(ab*ab*)2 3 0/R . A!"#$% |,,  3 ;g{,,(d'`FzFE-Qڛb>"JFIFKKMSO Palette C   ")$+*($''-2@7-0=0''8L9=CEHIH+6OUNFT@GHEC !!E.'.EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE"!!1AQqa!1 ?F3]'IƓe5,J$3?O 5LXyYL4tO%fxM\DXL`: a2HS=rtd+f\UtV5m7L?cf7 `Zx5\kt tudions la classe de machines abstraites que sont les automates tats finis rguliers. Chapitre 1 Quelques mots de V* sur V={a, b, c}: (, a, b, c, aa, ab, ba, bb, aaa, aab, abccbbaabcaacb, . V* cc > jbjbSS 3}11T@]wwwwD8(@|VTj(>=Q ,."Fw].]];8]Pwww] Xw$@|JWl~$ Annexe A Rponses aux exercices  TOC \o "1-3" \n \p " "  2.1 Automates d'tats finis Dfinition informelle Notations Reconnaissance d'un mot Dfinition formelle des automates finis dterministes Automates finis non-dterministe Automates avec (-transition quivalences d'automates 2.2 Transformation d'une expression rgulire en un automate Proprit Cas de base Rcurrence . limination des (-transitions 2.3 Transformation d'un automate en une expression rgulire Par rduction d'automates Parorrespond tous les mots quil est possible de faire avec des a, des b et des c. ( et dune faon gnrale tous les mots ne comportant pas de a. sinon, on peut avoir: abbbccbabcbc, aaaa, abcabc, mais on ne peut pas avoir: abc, aaa, babbaacc, L1 ( L2 = V*. L1 ( L2 = (. V*( L1 = L1. On a par exemple:1011, 1, 10000, 1111, L peut correspondre un codage binaire dentiers priv de 0. Lbis correspond un codage dentiers, 0 compris. ( ( ( ( ( (  PAGE 2 Chapitre 2 Automates detats finis et langages rguliers  PAGE 1                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 5 6 7 8 9 : ; < = > 6]<]6g8g@gjh,j6jDjFjjjnjrj~jjjjj$ . & FG.'3 0/R . A!"#$% |,,  3 ;g{,,(d'`FzFE-Qڛb>"JFIFKKMSO Palette C   ")$+*($''-2@7-0=0''8L9=CEHIH+6OUNFT@GHEC !!E.'.EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE"!!1AQqa!1 ?F3]'IƓe5,J$3?O 5LXyYL4tO%fxM\DXL`: a2HS=rtd+f\UtV5m7L?cf7 `Zx5\k 21 > 6]8]:]<]:gg@gfhhhjh(j*j,j4j6jBjFjdjfjjjjjjjjjjjjjjnnnppp"r$r&rH* jUmH0J:CJmH 0JCJmH*3 0/R . A!"#$% |,,  3 ;g{,,(d'`FzFE-Qڛb>"JFIFKKMSO Palette C   ")$+*($''-2@7-0=0''8L9=CEHIH+6OUNFT@GHEC !!E.'.EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE"!!1AQqa!1 ?F3]'IƓe5,J$3?O 5LXyYL4tO%fxM\DXL`: a2HS=rtd+f\UtV5m7L?cf7 `Zx5\k 221 On peut partir de l expression rgulire: b*(ab*)*2 Nombre de a impair.    2a b b a + b q1 a q2 q0 a + b b q1 a q2 q0 rsolution d'quations 2.4 Dterminisation et Minimisation Mthode de dterminisation Relation d'quivalence sur les langages rguliers 2.5 Autres oprations sur les automates Automate complmentaire Automate miroir Intersection de deux automates 2.6 Conclusion  Dans ce chapitre, nous prsentons et tudions la classe de machines abstraites que sont les automates tats finis rguliers. Chapitre 1 Quelques mots de V* sur V={a, b, c}: (, a, b, c, aa, ab, ba, bb, aaa, aab, abccbbaabcaacb, . V* correspond tous les mots quil est possible de faire avec des a, des b et des c. ( et dune faon gnrale tous les mots ne comportant pas de a. sinon, on peut avoir: abbbccbabcbc, aaaa, abcabc, mais on ne peut pas avoir: abc, aaa, babbaacc, L1 ( L2 = V*. L1 ( L2 = (. V*( L1 = L1. On a par exemple:1011, 1, 10000, 1111, L peut correspondre un codage binaire dentiers priv de 0. Lbis correspond un codage dentiers, 0 compris. ( ( ( ( ( (  PAGE 2 Chapitre 2 Automates detats finis et langages rguliers  PAGE 1                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 5 6 7 8 9 : ; < = > 6]<]6g8g@gjh,j6jDjFjjjnjrj~jjjjj$ . & FG.'3 0/R . A!"#$% |,,  3 ;g{,,(d'`FzFE-Qڛb>"JFIFKKMSO Palette C   ")$+*($''-2@7-0=0''8L9=CEHIH+6OUNFT@GHEC !!E.'.EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE"!!1AQqa!1 ?F3]'IƓe5,J$3?O 5LXyYL4tO%fxM\DXL`: a2HS=rtd+f\UtV5m7L?cf7 `Zx5\k 21 > 6]8]:]<]:gg@gfhhhjh(j*j,j4j6jBjFjdjfjjjjjjjjjjjjjjnnnppp"r$r&rRtZt\t^tH* jUmH0J:CJmH 0JCJmH.3 0/R . A!"#$% |,,  3 ;g{,,(d'`FzFE-Qڛb>"JFIFKKMSO Palette C   ")$+*($''-2@7-0=0''8L9=CEHIH+6OUNFT@GHEC !!E.'.EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE"!!1AQqa!1 ?F3]'IƓe5,J$3?O 5LXyYL4tO%fxM\DXL`: a2HS=rtd+f\UtV5m7L?cf7 `Zx5\k 221 jjjjjjjjnp&r'$ L1 sur V={a,b} terl que les mots aient un n et aobtenir l automate suivant:2 obtenir2 On peut partir de l expression rgulire: b*(ab*)*2 Nombre de a impair.    2a b b a + b q1 a q2 q0 a + b b q1 a q2 q0 jjjjjjjjnp&r^t'$ L1 sur V={a,b} terl que les mots aient un n et aobtenir l automate suivant:2 obtenir2 L1 sur V={a,b} te2